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CENTER OF MASS AND MOMENT OF INERTIA     163
126.  Routh's Rule.  The following is a useful rule for re-
membering the moments of inertia of certain types of bodies :
Moment of inertia with respect to any axis of symmetry
__              sum of the squares of the perpendicular semi-axes
" maSS X                           3^5~ --
The denominator of the right-hand member is 3, 4, or 5 ac-
cording as the body is rectangular, elliptical, or ellipsoidaL
The following illustrate Routh's rule.
Rectangular lamina; about axis perpendicular to its plane:
Circular lamina; about axis perpendicular to its plane:
J__
Elliptical lamina; about axis perpendicular to its plane:
Rectangular parallelepiped; about axis perpendicular to one of its sides :
tfjL !
T         44      a2 + &2 !___-_-.
Circular cylinder; about longitudinal axis: r         a? + a2     ma2
J = m___=__.
Sphere; about a diameter:
2   A
5        5
Ellipsoid; about one of its axes :